J. Gary Lutz

Curriculum-Based Measures and Performance on State Assessment and Standardized Tests Reading and Math Performance in Pennsylvania

General outcome measures (GOMs) provide educators with a means to evaluate student progress toward curricular objectives. Curriculum-based measurement (CBM) is one type of GOM that has a long history in the research literature with strong empirical support. With the increased emphasis on instruction linked to state standards and statewide achievement tests, the relationship between CBM and these measures has been called into question. This study examined the relationships between CBM of reading, math computation, and math concepts/applications and the statewide standardized achievement test as well as published norm-referenced achievement tests in two districts in Pennsylvania. Results showed that CBM had moderate to strong correlations with midyear assessments in reading and mathematics and both types of standardized tests across school districts. The data suggest that CBM can be one source of data that could be used to potentially identify those students likely to be successful or fail the statewide assessment measure.

The Relationship between Canonical Correlation Analysis and Multivariate Multiple Regression.

The similarities between multivariate multiple regression and canonical correlation analysis have been inconsistently acknowledged in the literature. The present article shows that, although the stated objectives of these two analyses seem different, aspects of the analyses themselves are mathematically equivalent. A multivariate multiple regression analysis that incorporates discriminant analysis as part of its post hoc investigation will produce identically the same results as a canonical correlation analysis in terms of omnibus significance testing, variable weighting schemes, and dimension reduction analysis. A numerical example is provided.

The Effects of Curriculum on the Sensitivity of Curriculum-Based Measurement in Reading

This study examined the effects of curriculum on the sensitivity of repeated curriculum-based measurement (CBM). Participants included 24 third-grade students who were instructed primarily in a literature-based Scott, Foresman basal series, and 24 third-grade students who were instructed primarily in a more traditional basal series. CBM passage probes from each basal reading series were administered to all students twice weekly over a 9-week period. Each students rate of progress in each reading series was indexed using an ordinary least squares regression to determine the slope of the data series. Results suggested that passage probes selected from the literature-based basal series were less sensitive to indexing growth over time than those from the traditional basal series.

Evaluation of Oral Reading Rate as a Curriculum-Based Measure Within Literature-Based Curriculum

Abstract This study investigated the utility of oral reading rate as a metric in monitoring students’ progress over time when instruction was occurring in a literature-based curriculum. Participants included 28 second-grade and 30 fifth-grade students who were currently receiving their primary reading instruction in a literature-based series. Curriculum-based measurement (CBM) probes were administered to these students twice a week over a 10-week period to monitor their progress in reading. Resulting data suggests that the CBM oral reading rate is an effective metric for use with students who are being instructed in a literature-based reading series.

A Method for Constructing Data Which Illustrate Three Types of Suppressor Variables

A method is presented for the construction of an artificial data set which will illustrate the behavior of the traditional, the negative, and the reciprocal suppressor variable in multiple regression analysis. It extends the method of Dayton (1972) and includes the previously unrecognized reciprocal suppression defined by Conger (1974).

Predictors of Social Skills for Preschool Children at Risk for ADHD: The Relationship Between Direct and Indirect Measurements

The relationship between direct and indirect measurements of social skills and social problem behaviors for preschool children at risk for attention deficit hyperactivity disorder (ADHD) was examined. Participants included 137 preschool children, aged 3 to 5 years, at risk for ADHD, who were participating in a larger study examining the effects of early intervention for young children. Teachers rated the social skills and social problems of the participants. Direct observation data of participants were also collected at preschool during free play. Results support previous research on social skills assessment and suggest that indirect and direct measures may not be measuring the same aspect of social skills. Thus, a variety of evaluation tools are necessary to comprehensively assess the social skills of preschool children with social challenges.

Are Published IDEA Hearing Officer Decisions Representative

The authors of this study examined published hearing officer decisions under the Individuals with Disabilities Education Act to determine whether they were representative of the frequency and outcomes for the larger group consisting of published decisions and the much greater number of unpublished decisions. An empirical analysis of the fully adjudicated hearing officer cases in six randomly selected states revealed that the published sample was variably and, in general, questionably representative of the overall group of such decisions in terms of frequency and outcomes across time. More specifically, in terms of frequency, the representativeness of the published decisions, although moderate for the nation, varied widely from one state to another and was markedly limited for most individual states on a year-by-year basis. In terms of outcomes, the representativeness of the published sample also varied from state to state and was particularly suspect on a year-by-year basis within most states. On a collapsed-years basis, there was a statistically significant difference between the study samples outcome distributions and those in three of the six states, and a questionable congruence with a fourth state. The likely reasons for the limited representativeness include incomplete submission by some state education agencies, inconsistent selection by the publisher, and variance in the categorization of the year and decision outcome. Although the authors recommend undertaking further research, they caution against the generalizability of published hearing officer decisions, particularly in examining longitudinal trends within individual states.

A Turbo Pascal Unit for Approximating the Cumulative Distribution Function of Roy'S Largest Root Criterion

A unit is described which approximates the cumulative distribution function of Roys largest root criterion using results given by Pillai (1965). Functions within the unit can be used to find cumulative (and tail) probabilities for a sample value of Roys criterion or the critical value of Roys criterion for a given level of significance. As the only approximations to this distribution currently exist in tabular or chart form, the unit has utility for both data analysts and programmers. A demonstration program is included.

Determining the Most Significant Parametric Function for a Given Linear Multivariate Hypothesis

After a hypothesis about some linear multivariate statistical model has been tested and rejected (e.g., in a MANOVA), many researchers employ simultaneous test procedures to locate the source(s) of the rejection. If the global test was conducted using Roy’s largest root criterion, then this procedure guarantees at least one linear combination of the model parameters relative to some linear combination of the dependent variables that is significantly different from its hypothesized value. This most significant parametric function is not always easy to find, however, because it may not manifest itself in simple or “obvious” functions. A general solution to this problem is presented along with a practical example of its application.

Determining the Most Significant Parametric Function for a Given Linear Hypothesis

After a hypothesis about some linear statistical model has been tested and rejected (e.g., in an ANOVA), many researchers employ the Scheffe procedure to locate the source(s) of the rejection. This procedure guarantees that there is at least one linear combination of the model parameters (consistent with the hypothesis) that is significantly different from its hypothesized value. This most significant parametric function is not always easy to find, however, because it may not manifest itself in simple functions (such as pairwise contrasts between groups) or in “obvious” functions (such as those suggested by the graph of an interaction). A general solution to this problem is presented along with a practical example of its application.